Excircle Formulae

Let us now turn our attention to excircles. For any triangle \(\Delta ABC\) , there will be three ex-circles. For examples, the ex-circle opposite to the angle A will touch the side BC and two sides AB and AC produced:

The ex-circle opposite to the angle A. The radius of this circle will be denoted by r1. Similarly, the radii of the other two circles are denoted by r2 and r3.

The next four relations are concerned with the ex-radii \({r_1},{r_2},{r_3}\) and how these relate to the other parameters of the triangle: